Answer:
y = 2(x-3)^2 -12
y = -4/9(x-2)^2 +7 bonus
Step-by-step explanation:
The vertex form of a parabola is
y = a(x-h)^2 + k where (h,k) is the vertex
y = a(x-3)^2 - 12
We have one point given (0,6)
6 = a (0-3) ^2 -12
6 = a (-3)^2 -12
6 = 9a-12
Add 12 to each side
6+12 = 9a
18 = 9a
Divide each side by 9
18/9 = 9a/9
a=2
y = 2(x-3)^2 -12
We follow the same steps for the bonus
y = a(x-2)^2 +7
Substitute the point into the equation
3 = a (-1-2)^2 +7
3 =a (-3)^2 +7
3 = 9a +7
subtract 7 from each side
3-7 = 9a +7-7
-4 = 9a
Divide by 9
-4/9 =a
y = -4/9(x-2)^2 +7
Answer:
Option C. The robin flies fastest because its rate is 15 m/s
Step-by-step explanation:
Let
x -----> the time in seconds
y ----> the distance in meters
The speed is equal to divide the distance by the time
In this problem, the slope or unit rate of the linear equation is the same that the speed
<em>Robin's Flight</em>
<em>Find the slope</em>
The formula to calculate the slope between two points is equal to
take two points from the table
(2,30) and (3,45)
substitute in the formula
<em>Cardinal's Flight</em>
<em>Blue Jay's Flight</em>
take two points from the graph
(0,0) and (2,20)
substitute in the formula
Compare
The robin flies fastest because its rate is 15 m/s
For ABC:
The interior angle of C is 180 - 142 = 38
The three interior angles add up to 180°
(2x - 15) + (x - 5) + 38 = 180
3x - 20 + 38 = 180
3x + 18 = 180
3x = 162
x = 54
The measure of angle ABC = x - 5 = 54 - 5 = 49
For JKL:
The interior angle of L is 180 - 100 = 80°
The 3 interior angles add up to 180°
(2x + 27) + (2x - 11) + 80 = 180
4x + 16 + 80 = 180
4x + 96 = 180
4x = 84
x = 21
The measure of angle JKL is 2x - 11 = 2(21) - 11 = 42 - 11 = 31°
Answer:
10 3/5
Step-by-step explanation:
6 4/5 + 3 4/5
First convert to improper fraction,
34/5 + 19/5
Then add the improper fractions,
=>53/5
Then convert improper fraction to mixed fraction,
=> 53/5 = 10 3/5
